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Prelim 2016 Maths Help Thread (1 Viewer)

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kawaiipotato

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Consider the function f(x)=(x^3+8x)/8
a. Show that f(x) is an increasing function
b. Find the equation of the tangent to y=f(x) at the origin
c. Using equal scales of axes, sketch a graph of y=f(x) over the domain -2=<x=<2 and draw its tangent at the origin
d. explain why an inverse exists and draw a grapg of y=f^-1(x) on your diagram
e. Solve f^-1(x)=8
f. Evaluate Integral of 3 to 0 f^-1(x) dx















































BTW Integrand just realised but you've been here all night lol
So?
 
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Green Yoda

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ICU trebla has asked you a question multiple times and very politely, and you have ignored. How do you expect us to answer about 60 question at once when you can't answer one?
 

DatAtarLyfe

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Consider the function f(x)=(x^3+8x)/8
a. Show that f(x) is an increasing function
b. Find the equation of the tangent to y=f(x) at the origin
c. Using equal scales of axes, sketch a graph of y=f(x) over the domain -2=<x=<2 and draw its tangent at the origin
d. explain why an inverse exists and draw a grapg of y=f^-1(x) on your diagram
e. Solve f^-1(x)=8
f. Evaluate Integral of 3 to 0 f^-1(x) dx
What parts of this don't you get?
Becoz a-c is basic for prelim
 

Simorgh

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I cant believe I made this thread and then hardly ever use it to help myself lel
 

fluffchuck

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Hey guys, how would you tackle this question?

It was proven in the notes above that the tangents to the parabola x2 = 4ay at two points
P(2ap, ap^2) and Q(2aq, aq^2) on the parabola intersect at the point M(a(p + q), apq).
Explain why this result can be restated as follows: ‘The tangents at two points on the
parabola x^2 = 4ay meet at a point whose x-coordinate is the arithmetic mean of the
x-coordinates of the points, and whose y-coordinate is one of the geometric means of the
y-coordinates of the points.’ Which geometric mean is it?

Thank you! :)
 

InteGrand

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Hey guys, how would you tackle this question?

It was proven in the notes above that the tangents to the parabola x2 = 4ay at two points
P(2ap, ap^2) and Q(2aq, aq^2) on the parabola intersect at the point M(a(p + q), apq).
Explain why this result can be restated as follows: ‘The tangents at two points on the
parabola x^2 = 4ay meet at a point whose x-coordinate is the arithmetic mean of the
x-coordinates of the points, and whose y-coordinate is one of the geometric means of the
y-coordinates of the points.’ Which geometric mean is it?

Thank you! :)
 

jathu123

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Not really a help post, but I found a couple of interesting trig questions if any of you prelim people wanna try it out


 

leehuan

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Hint for #2

Not really a help post, but I found a couple of interesting trig questions if any of you prelim people wanna try it out


Choose the more convenient cosine double angle expansion.
P.S. what is 1 equal to?
 

eyeseeyou

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The wording of this question is confusing the hell out of me:

If f(x)=e^(x+1) find the inverse function f^-1(x) and hence show that f(f^-1(x))=f^-1(f(x))=x

So far this was what I did:

f(x)=e^(x+1)
y=e^(x+1)
x=e^(y+1)
lnx=y+1
y=lnx-1
f^-1(x)=lnx-1

Thanks
 

leehuan

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The wording of this question is confusing the hell out of me:

If f(x)=e^(x+1) find the inverse function f^-1(x) and hence show that f(f^-1(x))=f^-1(f(x))=x

So far this was what I did:

f(x)=e^(x+1)
y=e^(x+1)
x=e^(y+1)
lnx=y+1
y=lnx-1
f^-1(x)=lnx-1

Thanks
And you're still trying to do inverse functions before knowing what actual functions are.

 
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